Question

À solução da equação 5x elevado a 2 + 2 x + 1= 0 no campo dos complexos é?

Answer 1

5x² + 2x + 1 = 0

Δ = b² - 4ac ⇒  Δ = 2² - 4.5.1 ⇒  Δ = 4 - 20 ⇒  Δ = - 16

Considere: √(- 1) = i

√(- 16) ⇒  √(- 1 * 16) ⇒  √(-1) * √(16) ⇒  i * 4 ⇒  4i 


$x= \dfrac{-b\pm \sqrt{\Delta}}{2a} \to~~~~ x= \dfrac{-2\pm \sqrt{-16}}{2.5} \to~~~~ x= \dfrac{-2\pm 4i}{10} \to\\\\\\ x'= \dfrac{-2+ 4i}{10} \to~~~~ \boxed{ x'= \dfrac{-1+ 2i}{5} } \\\\\\ x''= \dfrac{-2+ 4i}{10} \to~~~~ \boxed{ x''= \dfrac{-1- 2i}{5} }\\\\\\\\ \large\boxed{\boxed{ S=\left\{ \dfrac{-1- 2i}{5}~~;~~\dfrac{-1+ 2i}{5} \right\} }}$